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Constructing a boosted, spinning black hole in the damped harmonic gauge

Varma, Vijay and Scheel, Mark A. (2018) Constructing a boosted, spinning black hole in the damped harmonic gauge. Physical Review D, 98 (8). Art. No. 084032. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20181017-102934986

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Abstract

The damped harmonic gauge is important for numerical relativity computations based on the generalized harmonic formulation of Einstein’s equations and is used to reduce coordinate distortions near binary black hole mergers. However, currently there is no prescription to construct quasiequilibrium binary black hole initial data in this gauge. Instead, initial data are typically constructed using a superposition of two boosted analytic single black hole solutions as free data in the solution of the constraint equations. Then, a smooth time-dependent gauge transformation is done early in the evolution to move into the damped harmonic gauge. Using this strategy to produce initial data in the damped harmonic gauge would require the solution of a single black hole in this gauge, which is not known analytically. In this work we construct a single boosted, spinning, equilibrium black hole in damped harmonic coordinates as a regular time-independent coordinate transformation from Kerr-Schild coordinates. To do this, we derive and solve a set of four coupled, nonlinear, elliptic equations for this transformation, with appropriate boundary conditions. This solution can now be used in the construction of damped harmonic initial data for binary black holes.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.98.084032DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.084032PublisherArticle
https://arxiv.org/abs/1808.07490arXivDiscussion Paper
ORCID:
AuthorORCID
Varma, Vijay0000-0002-9994-1761
Additional Information:© 2018 American Physical Society. Received 27 August 2018; published 17 October 2018. This work was supported in part by the Sherman Fairchild Foundation and NSF Grants No. PHY-1404569, No. PHY-1708212, and No. PHY-1708213 at Caltech. The simulations were performed on the Wheeler cluster at Caltech, which is supported by the Sherman Fairchild Foundation and Caltech.
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSFPHY-1404569
NSFPHY-1708212
NSFPHY-1708213
Issue or Number:8
Record Number:CaltechAUTHORS:20181017-102934986
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181017-102934986
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90305
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Oct 2018 16:38
Last Modified:09 Mar 2020 13:19

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